Various techniques (e.g., electromagnetic or seismic techniques) exist to perform surveys of a subterranean structure for identifying subterranean bodies of interest. Examples of bodies of interest in the subterranean structure include hydrocarbon-bearing reservoirs, gas injection zones, thin carbonate or salt layers, and fresh-water aquifers. One type of electromagnetic (EM) survey technique is the controlled source electromagnetic (CSEM) survey technique, in which an electromagnetic transmitter, called a “source,” is used to generate electromagnetic signals. Surveying units, called “receivers,” are deployed on a surface (such as at the sea floor or on land) within an area of interest to make measurements from which information about the subterranean structure can be derived. The receivers may include a number of sensing elements for detecting any combination of electric fields, electric currents, and/or magnetic fields.
A seismic survey technique uses a seismic source, such as an air gun, a vibrator, or an explosive to generate seismic waves. The seismic waves are propagated into the subterranean structure, with a portion of the seismic waves reflected back to the surface (earth surface, sea floor, sea surface, or wellbore surface) for receipt by seismic receivers (e.g., geophones, hydrophones, etc.).
Measurement data (e.g., seismic measurement data or EM measurement data) is analyzed to develop a model of a subterranean structure. The model can include, as examples, a velocity profile (in which velocities at different points in the subterranean structure are derived), a density profile, an electrical conductivity profile, and so forth.
Conventionally, to update a model used in seismic or EM tomography of the subterranean structure, a linearized forward problem can be solved using a least squares technique, such as by using a least squares quadratic relaxation (LSQR) solver. However, should new information become available or if it becomes desirable to consider variations of prior information, then the least squares inversion would have to be repeated to update the model. Repeating the inversion is computationally very expensive.